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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 26, NO. 2, MAY 2011

Offline Detection, Identification, and Correction of Branch Parameter Errors Based on Several Measurement Snapshots Madeleine R. M. Castillo, Joao B. A. London,Jr., Member, IEEE, Newton Geraldo Bretas, Senior Member, IEEE, Serge Lefebvre, Jacques Prévost, and Bertrand Lambert

Abstract—This paper proposes a three-stage offline approach to detect, identify, and correct series and shunt branch parameter errors. In Stage 1 the branches suspected of having parameter errors are identified through an Identification Index (II). The II of a branch is the ratio between the number of measurements adjacent to that branch, whose normalized residuals are higher than a specified threshold value, and the total number of measurements adjacent to that branch. Using several measurement snapshots, in Stage 2 the suspicious parameters are estimated, in a simultaneous multiple-state-and-parameter estimation, via an augmented state and state vector for the parameter estimator which increases the inclusion of suspicious parameters. Stage 3 enables the validation of the estimation obtained in Stage 2, and is performed via a conventional weighted least squares estimator. Several simulation results (with IEEE bus systems) have demonstrated the reliability of the proposed approach to deal with single and multiple parameter errors in adjacent and non-adjacent branches, as well as in parallel transmission lines with series compensation. Finally the proposed approach is confirmed on tests performed on the Hydro-Québec TransÉnergie network.

V

Index Terms—Parameter error detection and identification, parameter estimation, power systems, state estimation.

I. INTRODUCTION A. Motivation HE STATIC state estimator (SE) is an essential power system operational tool in an energy management system (EMS), since its role is to provide a complete, coherent, and reliable network real-time model used to set up other EMS applications (e.g., contingency analysis, spot price calculation, and load forecasting function). The inputs of a conventional SE are a redundant collection of measurements and a mathematical model that relates these measurements to the nodal voltage magnitudes and phase angles, which are taken as the state variables of the system. This

T

Manuscript received March 09, 2010; revised March 12, 2010 and June 07, 2010; accepted July 16, 2010. Date of publication August 26, 2010; date of current version April 22, 2011. This work was supported by FAPESP and CNPQ. Paper no. TPWRS-00185-2010. M. R. M. Castillo, J. B. A. London, Jr., and N. G. Bretas are with the Sao Carlos Engineering School, University of Sao Paulo, Sao Carlos 03071-000, Brazil (e-mail: [email protected]; [email protected]; [email protected]). S. Lefebvre and J. Prévost are with the Institut de recherche d’HydroQuébec, Varennes, QC J3X1S1, Canada (e-mail: [email protected]; pré[email protected]). B. Lambert is with the TransÉnergie, division of Hydro-Québec, Montreal, QC H1P 3C6, Canada (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRS.2010.2061876

model is based on Kirchhoff’s and Ohm’s laws and relies on several assumptions, among which network configuration and associated parameters (e.g., transmission line series and shunt admittances, transformer tap position, transformer reactances, etc.) are considered perfectly known. Unfortunately, these assumptions do not hold true. Parameter errors can have adverse impact on the SE solutions and are less evident to detect than errors in network configurations (topology errors). Parameter errors may often stem from inaccurate manufacturing data, network changes not properly updated in the data base, wrong or oversimplified calculations, and so on [1], [2]. Although various branch parameter estimation approaches have been proposed, most of them address only transmission line series admittances and assume the influence of transmission line shunt admittances as being insignificant to state estimation solution [3], [4]. However, several papers have shown that influence is significant [5]–[7], mainly in transmission systems with a large circulation (absorption and compensation) of reactive power. This is the case of the Hydro-Québec’s transmission network. According to [8], Hydro-Québec TransÉnergie uses the SE to produce power flow base cases used to analyze the security of the transmission grid. Moreover, the SE usage at Hydro-Québec TransÉnergie is shifting from a strictly security function to one that includes economic considerations. Consequently, the estimated quantities must be as close as possible to their “true” values. In order to obtain a reliable SE, several studies have been performed at Hydro-Québec [6]–[8]; however, branch parameter errors (series and shunt admittances) validation (i.e., detection, identification, and correction) still represents a challenging task. A practical and efficient offline approach to detect, identify, and correct branch parameter errors (series and shunt admittances) is proposed in this paper. B. Literature Review The first task of a parameter estimation process is to identify the suspicious parameters, that is, the parameters suspected to be in error. Since the parameter errors have the same effect on the estimated state as a set of correlated errors acting on all measurements adjacent to the erroneous branch, the identification of suspicious parameters is usually carried out by residual sensitivity analysis [1], [4].

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According to [2], in the presence of branch parameter error, larger residuals appear mainly, but not only, in Measurements at Distance 1 (adjacent measurements). Larger residuals also appear in Measurements at Distance 2 and 3 (Measurements at Distance 2 are those directly related to Measurements at Distance 1, and so on). Techniques for network parameter estimation can be classified as follows: methods based on residual sensitivity analysis [9], [10], and methods augmenting the state vector (the usual state vector is augmented with additional variables representing suspicious parameters). Depending on the way the augmented state vector is estimated, the methods based on that vector can be divided into two groups: 1) those using the classical normal equations [11], [12], and 2) those using the Kalman filter theory [13], [14]. The advantages and disadvantages of the methods of both groups are presented in [1]. In [4] an offline method for dealing with series branch parameters was proposed. The idea is to create a state estimation process immune/less sensitive to erroneous parameters by exploring the concept of irrelevant/barely relevant branches. Supplementary strategies based on changing the measurement weights were formulated in order to deal with special cases in which the temporary creation of irrelevant/barely relevant branches causes network unobservability. Results with the IEEE 14-bus test system were presented to illustrate the application of this method. As local measurement redundancy is a fundamental requisite to the success of any estimation process [15], especially if parameters estimation is included, recently some papers have addressed the possibility of improving the parameter validation process via the utilization of synchronized phasor measurements [16], provided by phasor measurement units (PMU). The incorporation of PMU measurements to improve the parameters estimation process will be addressed in a further paper.

gence problems, the proposed augmented state-parameter estimator works in a simultaneous way, i.e., each loop of its iterative process is divided into two “half-loops”: one to update the state variables and another to update the suspicious parameters. Observe that other methodologies for branch parameter estimation which use several measurement snapshots based on an augmented state vector have been proposed. However, as presented in [1] and [2], those methodologies solve the augmented model in a different way. Stage 3 enables the validation of the estimates obtained in Stage 2 and is developed via a conventional WLS estimator. Several simulation results (with IEEE bus systems) have demonstrated the high correctness and reliability of the proposed approach to deal with single and multiple parameter errors in adjacent (those having a terminal bus in common) and non-adjacent branches. Finally the proposed approach is applied to two real-life subsystems of the Hydro-Québec TransÉnergie system. One of these tests shows the proposed approach enables the estimation of series and shunt admittances of parallel transmission lines with series compensation. The preliminary version of the proposed approach was presented in [3]. However that version did not enable the estimation of shunt admittances and was not applied to a real network.

C. Contribution

A. Conventional State Estimation Based on the Normal Equations

The main contribution of this paper is a practical and efficient offline approach for network branch parameter (series and shunt admittances) errors detection, identification, and correction. The proposed approach deals with electrical parameters involved in the classical steady-state -equivalent modeling of transmission lines and consists of three stages. In comparison with other methodologies already proposed for branch parameters validation, the novel features of the proposed approach are the identification procedure of suspicious branches and the way the augmented state-parameter estimation problem is solved. In Stage 1 of the proposed approach, the suspicious branches are identified through an Identification Index (II) (the II of a branch is the ratio between the number of measurements adjacent to that branch, whose normalized residuals are higher than a specified threshold value and the total number of measurements adjacent to that branch). Using several measurement snapshots, the suspicious parameters are estimated in Stage 2. In order to do that, an augmented state vector state-parameter estimator, which increases the for the inclusion of suspicious branch parameters, is proposed and sequentially processed for each snapshot. To avoid conver-

D. Organization of the Paper The paper is organized as follows: Section II summarizes the state and parameter estimation fundamentals, Section III describes the proposed offline approach, Section IV presents the numerical results of the application of the proposed approach to benchmark networks for state estimation studies (IEEE bus systems), Section V highlights the application of the proposed approach to two real-life subsystems of the Hydro-Québec system, and Section VI presents the conclusions and final remarks. II. STATE AND PARAMETER ESTIMATION FUNDAMENTALS

A general state estimation model is given by (1) is the measurement vector , is the state vector ; is the nonlinear state estimation function that reis the number lates the measurements to the system states; of state variables to be estimated; is the number of available measurements; and is the measurement error usually considered random Gaussian variable with zero mean and covariance matrix . Through the conventional WLS approach, the objective is to find the -vector that minimizes the index , defined as follows: where

(2) where the state vector Jacobian matrix equations:

is estimated by recursively forming the , and solving the normal (3)

with

(the gain matrix).

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B. Residual Analysis The residual vector , defined as being the difference between and the corresponding filtered quantities , is normalized and submitted to a validation test

(4) where

is the largest among all ; is the standard deviation of the th component of the residual vector, and is the residual covariance matrix given by (5) , the measurement with a gross error is detected If and the th measurement will be the one with gross error (usu[1]). ally C. Linking Measurement Residuals to Parameter Error A parameter error has the same effect on the estimated state as a set of correlated errors acting on all measurements adjacent to the erroneous branch (namely the power flows through the branch and the power injections at the end nodes), which results from a simple manipulation of the basic measurement model [1], [10]:

(6) where subscript refers to the involved measurements, is the true state vector, is the true value of the parameter of concern, is the erroneous value of the parameter. and Clearly the term in brackets in (6) acts as an equivalent additional measurement error. If the parameter error is large enough, this term may lead to bad data being detected and, when it occurs, the adjacent measurements will likely have the largest normalized residuals. The equivalent measurement error can be linearized as (7) where is the parameter error. Therefore, those branches whose normalized residuals of the adjacent measurements are larger than a specified threshold should be declared suspicious. D. Parameter Estimation Based on State Vector Augmentation In this class of methods, the suspicious parameters are additional state variables. Therefore, within the context of WLS estimation, the augmented estimation aims at minimizing the objective function (8) with respect to tions are

and . Now, the first-order optimality condi(9a) (9b)

Fig. 1. Flowchart of the proposed approach.

where and are the Jacobian matrices of with respect to and , respectively. A distinction can be made according to whether and are determined simultaneously or sequentially. III. PROPOSED APPROACH The proposed offline approach comprises three stages: Stage 1—Identification of suspicious branches; Stage 2—Estimation of suspicious parameters; and Stage 3—Validation of suspicious parameter estimates. All of them will be presented in the following. Fig. 1 presents the flowchart of the proposed approach, where LSB is a List of Suspicious Branches and LSBE is a List of Suspicious Branches whose parameters were Estimated and Validated. A. Stage 1—Identification of Suspicious Branches As the proposed approach is offline, it is possible to select particular recorded snapshots free from both bad data and topological errors. Consequently, measurements with larger normalized residuals indicate the presence of parameter errors. In some researches, the identification of suspicious parameters is performed analyzing only the measurements that present the largest normalized residuals. However, when there are several measurements adjacent to parameter errors, there is no guarantee that the largest normalized residual will correspond to one of those measurements. In order to reduce the risk of misidentifying suspicious branches, the proposed approach

CASTILLO et al.: OFFLINE DETECTION, IDENTIFICATION, AND CORRECTION OF BRANCH PARAMETER ERRORS

uses three vectors: Measurement-to-Branch Vector (MBV), Suspicious-Branches Vector (SBV), and Identification-Index , where is Vector (IIV), all of them with dimension the number of branches of the system. MBV shows how many measurements are adjacent to each indicates that there are branch of the system [ measurements adjacent (or related) to branch ].1 SBV indicates how many measurements adjacent to each branch have normalized residuals higher than a specified threshold [ indicates that there are measurements adjacent to branch with normalized residual higher than a specified threshold]. Each element of IIV is the ratio between the corresponding elements of . All the SBV and MBV, that is, branches with will be classified as suspicious. However, the first parameters to be estimated are the ones of . those branches with Considering those three vectors, the proposed algorithm for the identification of suspicious branches can be summarized as follows. Step 1) For a given measurement snapshot, initialize the MBV. Step 2) Run the conventional WLS state estimator and obtain the measurement normalized residuals. Step 3) If there are normalized residuals higher than a specified threshold, go to the next step (this value is usually equal to 3 [1]). Otherwise, end the algorithm. Step 4) Through the measurements with the normalized residuals higher than the specified threshold, initialize the SBV and compute IIV. Step 5) Form a list of suspicious branches, sorted according to the value of the corresponding IIV elements. If there exist suspicious branches with the same IIV, the branch with the highest normalized residual will be considered the most suspicious. B. Stage 2—Estimation of Suspicious Parameters The proposed procedure for the estimation of suspicious parameters is offline, uses several measurement snapshots in a sequential way, and an augmented state-parameter estimator which increases the state vector for the inclusion of suspicious branch parameters (series and shunt admittances). The normal equations technique is used to deal with the augmented model. Next all the characteristics of the proposed procedure will be analyzed in details. 1) Offline: According to the literature [1], [2], for the estimation of parameters that remain constant for a long period of time, such as line parameters, it is suggested that the estimation should occur offline, through the utilization of measurements of several measurement snapshots. One important advantage of an offline parameter estimation procedure is the possibility of choosing measurement snapshots with controlled redundancy and accuracy level and free from both bad data and topological errors. 2) Several Measurement Snapshots: When seeking for an accurate line parameter estimate, better results can be obtained 1A measurement is adjacent (or related) to a branch if it is either a power flow measurement at that branch or a power injection measurement at the terminal nodes of that branch.

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using several measurement snapshots, say, , taken at different time instants. As a consequence, the objective function (2) becomes

(10) and . and has to be minimized with respect to In order to reduce the computational effort to solve (10), the proposed offline procedure for the estimation of suspicious parameters processes the measurement snapshots in a sequential way. In general, the following procedure is proposed. Snapshot 1: initialize all bus voltages at flat start and the suspicious parameters with the available values. Consid, esering the measurements available in this snapshot state variables and the suspicious timate the parameters , using the augmented state-parameter estimator mentioned above. Snapshot 2: initialize all bus voltages at flat start (as in snapshot 1), but the suspicious parameters are now initialized with the values estimated in the previous snapshot . Considering the measurements available in this snap, estimate the state variables and the shot . suspicious parameters The stopping criterion of the proposed procedure is the comparison between the magnitude of the suspicious parameter correction vector, obtained in two sequential snapshots , and a pre-established limit for the corrections. In this paper, whenever a suspicious parameter correction obtained is below 0.01, in two sequential snapshots the corresponding parameter is removed from the augmented vector, that is, the estimated value converges to the correct pa. rameter value The proposed procedure can be viewed as an “adaptive” filter since the parameter estimate improves as increases. 3) Simultaneous State-and-Parameter Estimation: The proposed augmented state-parameter estimator will be applied to each recorded snapshot. As a consequence, for each measurestate vector with the ment snapshot it increases the suspicious branch parameters . The proposed augmented state-parameter estimator is based on the formulation presented in Section II-D. There exist two possibilities to estimate the augmented state vector from the measurement vector available in a given snapshot. It can be estimated in either a simultaneous or sequential way. In the simultaneous way, (9) are solved simultaneously for and , using the basic Newton-Raphson iterative process. On the other hand, in the sequential way, (9a) is solved with fixed, which amounts to solve a standard state estimation problem. The successive parameter adaptations and state re-estimation can be viewed as an “outer loop” that includes the state estimator. Our experience has shown that solving (9) in a sequential way has poor convergence. Consequently, the proposed augmented state-parameter estimator works in a simultaneous way, i.e., each loop of its iterative process is divided into two “halfstate variables and another to loops”: one to update the update the suspicious parameters.

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The steps of the proposed augmented state-parameter estimator algorithm are given below: . Step 1) Start iterations, set the iteration index Step 2) Initialize all bus voltages at flat start and the suspicious parameter vector considering the available values. . Step 3) Solve Step 4) Update . Step 5) Solve . and are lower than the converStep 6) Check if gence tolerance. If so, stop. Else, continue. and ; go to step Step 7) Update: 3. C. Stage 3—Validation of Suspicious Parameter Estimates This stage is necessary because, due to the parameter error smearing effect, in the identification process of suspicious branches (Stage 1), it is possible to incorrectly classify one branch as suspicious. In order to validate the suspicious parameter estimate, a conventional WLS estimator is processed considering the same measurement snapshot processed in Stage 1 and the estimated values obtained in Stage 2. After that, the IIV of that suspicious branch is calculated again. If this IIV does not decrease in relation to that obtained in Stage 1, it means that branch was incorrectly indicated as suspicious. Otherwise, that estimate is validated.

TABLE I SIMULATION RESULTS—IEEE 30-BUS SYSTEM

TABLE II SIMULATION RESULTS—IEEE 57-BUS SYSTEM

IV. RESULTS OF TESTS ON BENCHMARKS This section presents the numerical results of the application of the proposed offline approach to the IEEE 30- and 57-buses systems (the topologies and parameters of these systems can be downloaded from [17]). Several simulations have been carried out using those systems. However, due to space limitations, only two representative scenarios will be presented here. In order to execute the tests, the initial conditions were constructed in the following way: To simulate measurements of several snapshots, a temporary evolution of the system load associated with one typical load profile was considered; Measurement values of each snapshot: these values were obtained from to which normally distributed an exact load flow solution noise was added. The measurement noise was assumed to be a random Gaussian variable with zero mean and standard de, where is the meter viation “ ” given by precision (in this paper ). In order to apply the proposed approach, 20 sets of measurements were generated to simulate 20 consecutive snapshots to each system. For the following tables, the parameters values are in p.u. and —series conducthe following nomenclature is used: tance (susceptance) of the branch from bus “a” to bus b; and —shunt susceptance of the branch from bus “a” to bus b. A. Test With the IEEE 30-Bus System In this test, multiple parameter errors are added simultaneously to the parameters of branches 1-2, 2-4, and 8-28. Observe that branches 1-2 and 2-4 are adjacent, that is, they have a

terminal bus in common. A highly redundant metering system was considered in this test, that is, all power and voltage magnitude measurements were considered available (global redundancy (m/N) of 3.79 for each measurement snapshot). Table I presents the correct values, the initial values, and the estimated values of the parameters of those branches. The values of all estimated parameters were corrected, mainly the series susceptance of branch 8-28 (from 30% to below 0.2923% of error). B. Test With the IEEE 57-Bus System In this test, multiple parameter errors are added simultaneously to the parameters of branches 7-8, 1-15, and 3-15. The measurement system used in this test does not consider the availability of all power and voltage measurements. Actually, no power injection measurement is considered; only 296 power flow and 43 voltage magnitude measurements are considered available [global redundancy (m/N) of 3.00 for each measurement snapshot]. Table II presents the correct values, the initial values, and the estimated values of the parameters of those branches. The values of all estimated parameters were corrected, mainly the series susceptance of branch 1-15 (from 30% to below 0.1993% of error). V. RESULTS OF TESTS ON A REAL NETWORK A. Test Systems This section presents the numerical results of the application of the proposed offline approach to two real-life subsystems

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Fig. 4. Representation of one line of Subsystem 2.

Fig. 2. Subsystem 1.

Fig. 3. Subsystem 2.

of the Hydro-Québec system. Those subsystems are monitored from the main control center (CCR) of TransÉnergie, a division of Hydro-Québec, and were chosen to be analyzed because, by using the method for detecting and identifying topology and parameter errors presented in [18], they were considered suspected of having branch parameter errors. The first subsystem (Subsystem 1), whose one-line diagram is depicted in Fig. 2, consists of three buses and three 315-KV transmission lines: the first with 46 Km between stations 315-3 and 315-2 (branch L315-3); the second with 83 Km between stations 315-2 and 315-1 (branch L315-2); and the third with 130 Km between stations 315-3 and 315-1 (branch L315-1). As can be seen in Fig. 2, Subsystem 1 is provided with voltage magnitude measurements in all the three buses and with pairs of active and reactive power flows in all the three lines, on both sides, yielding a total of 15 measurements. The second subsystem (Subsystem 2), whose one-line diagram is depicted in Fig. 3, consists of two buses and three parallel 735-KV transmission lines. Subsystem 2 will be used to show that, by using the proposed approach, it is possible to estimate the series and shunt admittances of those lines via two-terminal data. According to Fig. 3, Subsystem 2 is provided with voltage magnitude measurements in the two buses and with pairs of active and reactive power flows in all the three lines, on both sides, yielding a total of 14 measurements. As can be seen in Fig. 3, Subsystem 2 has series compensation devices located at location R. The compensation device is a simple capacitor bank (Xc is known). The distance between station 735-1 and location R (segment LR) is 242 Km, and the

distance between station 735-2 and location R (segment RM) is 137 Km. In order to apply the proposed approach to Subsystem 2, each of its lines is represented as illustrated in Fig. 4 [19]. equivIn Fig. 4, the following notations are adopted: alent series impedance of the line segments LR and RM, respec, equivalent shunt admittances of the line segtively, and ments LR and RM, respectively. Referring to Fig. 4, the line segment LR, on the left of the compensation device, can be analyzed as a Delta circuit A. In the same way, the line segment RM can be analyzed as a Delta circuit B. Consequently, using the known value of Xc and applying successively delta-Y and Y-delta conversions to both delta circuits A and B, one obtains the equivalent steady-state -equivalent model of each of the three transmission lines of Subsystem 2. The proposed offline approach will be applied to estimate the parameters of the equivalent steady-state -equivalent model of those three transmission lines. Consequently, for each measurement snapshot that will be processed by the proposed approach, there will be 12 variables to be estimated, i.e., nine line parameters (shunt admittance, series conductance, and susceptance for each of the three lines), two voltage magnitudes (in both stations 735-1 and 735-2), and one voltage phase angle (in the station 735-2). After the estimation of the three line parameters of each of the three lines, it is possible to obtain the line parameters of each of the line segments LR and RM following the process described in the last paragraph. B. Simulation Data The simulations reported hereafter were performed with realtime data obtained from the SCADA system of the CCR of TransÉnergie. The measurement snapshots considered in the simulations were obtained within a time interval of 5 min. According to the experience of the system operators, the measurement snapshots used by the proposed offline approach are free from both bad data and topology errors. The following standard deviation values (used for weighting the measurements) are adopted: . for active power measurements, . for reactive power measurements, and . for voltage magnitude measurements. C. Validation of Simulation Results As the parameter true values are not known, to validate the results obtained via the proposed offline approach, the WLS performance index , given by (2), will be calculated for several

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TABLE III SIMULATION RESULTS—SUBSYSTEM 1

Fig. 5. Ratio J

(X )=J

TABLE IV SIMULATION RESULTS—SUBSYSTEM 2

(X ) (Smoothing)—Subsystem 1.

measurement snapshots considering both the available paramand the estimated parameter values eter values . In order to do that, a commercial state estimator available in the CCR of TransÉnergie will be used. The estimated parameter values will be considered validated if the ratio is higher than 1. D. Simulations For the following tables, the parameters values are in p.u. and —series conducthe following nomenclature is used: —shunt sustance (susceptance) of the branch “kl”; and ceptance of the branch “kl”. Subsystem 1: Table III presents the initial values (available in the data base) and the estimated values of the parameters of Subsystem 1 that were identified as suspect of having parameters errors. The branch L315-2 was not identified as suspect of having parameters errors by the proposed methodology (the available values are 4.001290-j41.793212 and 0.50857). As a consequence, those parameters were not estimated by the proposed methodology. 1) Validation of Simulation Results: Fig. 5 plots the ratio obtained for each operation point (every 5 min) during a day (September 24, 2009). Observe that, as for all operation points that ratio is higher than 1, the estimated parameter values are validated. Subsystem 2: Table IV shows the results of the application of the proposed approach to Subsystem 2. It is important to highlight that for this subsystem, there are big differences in the values of reactive power measurements obtained in consecutive snapshots. As a consequence, only one measurement snapshot was considered in this simulation in order to apply the proposed approach (August 7 at 2:29 am). 2) Validation of Simulation Results: Fig. 6 plots the ratio obtained for each operation point (every 5 min) during a day (September 26, 2009). Observe

Fig. 6. Ratio J

(X )=J

(X ) (Smoothing)—Subsystem 2.

that, as for all operation points that ratio is higher than 1, the estimated parameter values are validated. E. Analysis of Simulations Results As can be seen in Figs. 5 and 6, using the proposed offline approach, it was possible to improve the parameter values of two real-life subsystems. It is important to highlight that the simulation results are used to update the parameter values available in the data base in the CCR of TransÉnergie. This process also involves double-checking any discrepancies with the field data. VI. CONCLUSIONS This paper has presented a practical and efficient offline approach to detect, identify, and correct branch parameter errors (series impedance and shunt admittances). Actually the proposed method is an extension of the one proposed in [3]. Several simulation results of the application of the proposed approach to benchmark networks for state estimation studies (IEEE bus systems) have demonstrated the high accuracy and reliability of the proposed approach to deal with single and multiple parameter errors in adjacent and non-adjacent branches. The proposed approach was also demonstrated on tests performed on the Hydro-Québec TransÉnergie networks. One of

CASTILLO et al.: OFFLINE DETECTION, IDENTIFICATION, AND CORRECTION OF BRANCH PARAMETER ERRORS

these tests shows that the proposed approach enables the validation of series and shunt admittances of parallel transmission lines with series compensation.

REFERENCES [1] A. Abur and A. G. Expósito, Power System State Estimation: Theory and Implementation. New York: Marcel Dekker, 2004. [2] P. Zarco and A. G. Expósito, “Power system parameter estimation: A survey,” IEEE Trans. Power Syst., vol. 15, no. 1, pp. 216–222, Feb. 2000. [3] M. R. M. Castillo, J. B. A. London Jr, and N. G. Bretas, “Power system branch parameter error identification and estimation,” in Proc. Power and Energy Soc. General Meeting, Calgary, AB, Canada, Jul. 2009, pp. 1–8. [4] M. B. Do Coutto Filho, J. C. Stacchini de Souza, and E. B. M. Meza, “Off-Line validation of power network branch parameters,” IET Gen., Transm., Distrib., vol. 2, no. 6, pp. 892–905, 2008. [5] R. Mínguez and A. J. Conejo, “State estimation sensitivity analysis,” IEEE Trans. Power Syst., vol. 22, no. 3, pp. 1080–1091, Aug. 2007. [6] S. Lefebvre, J. Prévost, H. Horisberger, B. Lambert, and L. Mili, “Coping with Q-V solutions of the WLS state estimator induced by shunt-parameter errors,” in Proc. 8th Int. Conf. Probabilistic Methods Applied to Power Systems, Ames, IA, Sep. 12–16, 2004. [7] S. Lefebvre, J. Prévost, H. Horisberger, and B. Lambert, “On the accuracy of state estimation,” in Proc. Power Eng. Soc. Meeting, 2006. [8] S. Lefebvre, J. Prévost, J. C. Rizzi, P. Ye, B. Lambert, and H. Horisberger, “Operational experience with state estimation at hydro-Québec,” in Proc. IEEE Power and Energy Soc. General Meeting—Conversion and Delivery of Electrical Energy in the 21st Century, 2008, Jul. 20–24, 2008, pp. 1–8. [9] W. Liu, F. Wu, and S. Lun, “Estimation of parameter errors from measurement residuals in state estimation,” IEEE Trans. Power Syst., vol. 7, no. 1, pp. 81–89, Feb. 1992. [10] T. Van Cutsem and V. Quintana, “Network parameter estimation using online data with application to transformer tap settings,” Proc. Inst. Elect. Eng., vol. 135, pp. 31–40, Jan. 1988. [11] P. Zarco and A. G. Expósito, “Off-Line determination of network parameters in state estimation,” in Proc. 12th Power System Computation Conf., Dresden, Germany, Aug. 1996, pp. 1207–1213. [12] J. B. A. London Jr, L. Mili, and N. G. Bretas, “An observability analysis method for a combined parameter and state estimation of a power system,” in Proc. Int. Conf. Probabilistic Methods Applied to Power Systems, 2004, Sep. 12–16, 2004, pp. 594–599. [13] A. Debs, “Estimation of Steady-State power system model parameters,” IEEE Trans. Power App. Syst., vol. PAS-93, pp. 1260–1268, Sep./ Oct. 1974. [14] I. Slutsker and K. Clements, “Real time recursive parameter estimation in energy management systems,” IEEE Trans. Power Syst., vol. 11, no. 3, pp. 1393–1399, Aug. 1996. [15] J. B. A. London, L. F. C. Alberto, and N. G. Bretas, “Analysis of Measurement-Set qualitative characteristics for State-Estimation purposes,” IET Gen., Transm., Distrib., vol. 1, pp. 39–45, Jan. 2007. [16] J. Zhu and A. Abur, “Improvements in network parameter error identification via synchronized phasors,” IEEE Trans. Power Syst., vol. 25, no. 1, pp. 44–50, Feb. 2010. [17] Power System Test Case Achieve: University of Washington. [Online]. Available: htpp://www.ee.washington.edu/research/pstca. [18] M. H. Vuong, S. Lefebvre, and X. D. Do, “Detection and estimation of topology and parameter errors from Real-Time measurements,” in Proc. 2002 IEEE Power Eng. Soc. Summer Meeting, Jul. 2002, vol. 3, pp. 1565–1569.

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[19] Y. Liao, “Some algorithms for transmission line parameter estimation,” in Proc. 41st Southeastern Symp. System Theory, University of Tennessee Space Institute, Tullahoma, TN, Mar. 15–17, 2009. Madeleine R. M. Castillo received the B.S.E.E. degree from San Agustin National University of Arequipa, Arequipa, Perú, in 2002 and the M.S.E.E. degree from E.E.S.C.—University of Sao Paulo, Sao Paulo, Brazil, in 2006, both in electrical engineering. She is currently pursuing the Ph.D. degree at University of Sao Paulo. Her research interest includes parameter estimation of line transmission and state estimation in electrical power systems.

Joao B. A. London, Jr. (S’97–M’02) received the B.S.E.E. degree from the Federal University of Mato Grosso, Cuiabá, Brazil, in 1994, the M.S.E.E. degree from E.E.S.C.—University of Sao Paulo, Sao Paulo, Brazil, in 1997, and the Ph.D. degree from E.P.—University of Sao Paulo in 2000, all of them in electrical engineering. He is currently an Assistant Professor at the E.E.S.C.—University of Sao Paulo. His main areas of interest are power system state estimation, distribution system reconfiguration, and application of sparsity techniques to power system analysis.

Newton Geraldo Bretas (M’76–SM’89) received the Ph.D. degree from the University of Missouri, Columbia, in 1981. He became a Full Professor of the University of Sao Paulo, Sao Paulo, Brazil, in 1989. His work has been primarily concerned with power system analysis, transient stability using direct methods, as well as power system state estimation. he also has interest in energy restoration using ANN and GA for distribution systems.

Serge Lefebvre received the B.Sc.A. and M.Sc.A. degrees in electrical engineering from Ecole Polytechnique, Montreal, QC, Canada, and the Ph.D. degree from Purdue University, West Lafayette, IN. He has worked at the Research Institute of Hydro-Quebec (IREQ) since 1981 while being an Associate Professor at Ecole Polytechnique and University of Sherbrooke. He is presently a research project leader in the area of transmission and distribution. His current research activities are centered on energy management systems. Dr. Lefebvre served as the Chairman of the working group “Dynamic performance and modeling of dc systems and power electronics for transmission systems”.

Jacques Prévost received the B.Eng. degree in electrical engineering from Ecole Polytechnique in 1989. In 1989, he joined Hydro-Québec, where he has worked on power system applications for transmission planning. In 1998, he joined Hydro-Quebec’s Research Institute (IREQ). He is involved in power system applications for transmission operation.

Bertrand Lambert received the B.Eng. degree in electrical engineering from École Polytechnique de Montréal in 2001. Since then, he has worked for HydroQuébec TransÉnergie at the CCR, Hydro-Québec TransÉnergie main control room, as a network engineer. He is involved in helping Hydro-Québec’s dispatchers during daily operations and in the CCR EMS applications, especially the LASER system (state estimator, contingency analysis, power flow, and optimal power flow)